What is the equation of a quadratic function whose graph passes through (2, 0),

vazelinahS

vazelinahS

Answered question

2021-11-05

What is the equation of a quadratic function whose graph passes through (2, 0), (5, 0), and (3, -8)? Write your equation in standard form.

Answer & Explanation

falhiblesw

falhiblesw

Skilled2021-11-06Added 97 answers

Step 1 
Consider the given: 
The graph passes through (2,0), (5,0) and (3,−8). 
Let the equation is y=ax2+bx+c 
Consider the point (2,0), 
a(2)2+b(2)+c=0 
1) 4a+2b+c=0 
Consider the point (5,0), 
a(5)2+b(5)+c=0 
2) 25a+5b+c=0 
Consider the point (3, -8), 
a(3)2+b(3)+c=8 
3) 9a+3b+c=8 
Step 2 
From equation (1) and (2), 
4a+2b+c=25a+5b+c 
4a+2b=25a+5b 
4a25a=5b2b 
21a=3b 
7a=b 
From equation (1), 
4a+2b+c=0 
4a+2(7a)+c=0 
4a14a+c=0 
10a+c=0 
c=10a 
Step 3 
Substitute the value of b and c in equation (3). 
9a+3b+c=8 
9a+3(7a)+(10a)=8 
9a21a+10a=8 
21a+19a=8 
2a=8 
a=4 
b=7a 
b=7(4) 
b=28 
c=10a 
c=10(4) 
c=40 
Hence, 
The quadratic function equation is as follows:
y=4x228+40

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